Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.     

Forecasting realized volatility of agricultural commodities

We forecast the realized and median realized volatility of agricultural commodities using variants of the heterogeneous autoregressive (HAR) model. We obtain tick-by-tick data on five widely-traded agricultural commodities (corn, rough rice, soybeans, sugar, and wheat) from the CME/ICE. Real out-of-sample forecasts are produced for between 1 and 66 days ahead. Our in-sample analysis shows that the variants of the HAR model which decompose volatility measures into their continuous path and jump components and incorporate leverage effects offer better fitting in the predictive regressions. However, we demonstrate convincingly that such HAR extensions do not offer any superior predictive ability in their out-of-sample results, since none of these extensions produce significantly better forecasts than the simple HAR model. Our results remain robust even when we evaluate them in a Value-at-Risk framework. Thus, there is no benefit from including more complexity, related to the volatility decomposition or relative transformations of the volatility, in the forecasting models.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange,stock, and bond markets

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We find that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Out-of-sample forecasting experiments confirm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.     

Out-of-sample prediction of Bitcoin realized volatility: Do other cryptocurrencies help?

Inspired by cross-market information flows among international stock markets, we incorporate external predictive information from other cryptocurrency markets to forecast the realized volatility (RV) of Bitcoin. To make the most of such external information, we employ six widely accepted approaches to construct predictive models based on multivariate information. Our results suggest that the scaled principal component analysis (SPCA) approach steadily improves the predictive ability of the prevailing heterogeneous autoregressive (HAR) benchmark model considering both the model confidence set (MCS) test and the Diebold–Mariano (DM) test based on three widely accepted loss functions. The forecasting performance is persistent to various robustness checks and extensions. Notably, a mean–variance investor can obtain steady positive economic gains if the investment portfolio is constructed on the basis of the forecasts from the HAR-SPCA model. The results of this study show that external predictive information is statistically and economically important in forecasting Bitcoin RV.     

Stock market volatility forecasting: Do we need high-frequency data?

The general consensus in the volatility forecasting literature is that high-frequency volatility models outperform low-frequency volatility models. However, such a conclusion is reached when low-frequency volatility models are estimated from daily returns. Instead, we study this question considering daily, low-frequency volatility estimators based on open, high, low, and close daily prices. Our data sample consists of 18 stock market indices. We find that high-frequency volatility models tend to outperform low-frequency volatility models only for short-term forecasts. As the forecast horizon increases (up to one month), the difference in forecast accuracy becomes statistically indistinguishable for most market indices. To evaluate the practical implications of our results, we study a simple asset allocation problem. The results reveal that asset allocation based on high-frequency volatility model forecasts does not outperform asset allocation based on low-frequency volatility model forecasts.     

Adding dummy variables: A simple approach for improved volatility forecasting in electricity market

This study used dummy variables to measure the influence of day-of-the-week effects and structural breaks on volatility. Considering day-of-the-week effects, structural breaks, or both, we propose three classes of HAR models to forecast electricity volatility based on existing HAR models. The estimation results of the models showed that day-of-the-week effects only improve the fitting ability of HAR models for electricity volatility forecasting at the daily horizon, whereas structural breaks can improve the in-sample performance of HAR models when forecasting electricity volatility at daily, weekly, and monthly horizons. The out-of-sample analysis indicated that both day-of-the-week effects and structural breaks contain additional ex ante information for predicting electricity volatility, and in most cases, dummy variables used to measure structural breaks contain more out-of-sample predictive information than those used to measure day-of-the-week effects. The out-of-sample results were robust across three different methods. More importantly, we argue that adding dummy variables to measure day-of-the-week effects and structural breaks can improve the performance of most other existing HAR models for volatility forecasting in the electricity market.     

Forecasting realized volatility: a Bayesian model‐averaging approach

How to measure and model volatility is an important issue in finance. Recent research uses high‐frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model‐averaging approach to forecast realized volatility. Candidate models include autoregressive and heterogeneous autoregressive specifications based on the logarithm of realized volatility, realized power variation, realized bipower variation, a jump and an asymmetric term. Applied to equity and exchange rate volatility over several forecast horizons, Bayesian model averaging provides very competitive density forecasts and modest improvements in point forecasts compared to benchmark models. We discuss the reasons for this, including the importance of using realized power variation as a predictor. Bayesian model averaging provides further improvements to density forecasts when we move away from linear models and average over specifications that allow for GARCH effects in the innovations to log‐volatility. Copyright © 2009 John Wiley & Sons, Ltd.     

Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model

In this paper, we investigate the relation between time-varying risk aversion and renminbi exchange rate volatility using the conditional autoregressive range-mixed-data sampling (CARR-MIDAS) model. The CARR-MIDAS model is a range-based volatility model, which exploits intraday information regarding the intraday trajectory of the price. Moreover, the model features a MIDAS structure allowing for time-varying risk aversion to drive the long-run volatility dynamics. Our empirical results show that time-varying risk aversion has a significantly negative effect on the long-run volatility of renminbi exchange rate. Moreover, we observe that both intraday ranges and time-varying risk aversion contain important information for forecasting renminbi exchange rate volatility. The range-based CARR-MIDAS model incorporating time-varying risk aversion provides more accurate out-of-sample forecasts of renminbi exchange rate volatility compared to a variety of competing models, including the return-based GARCH, GARCH-MIDAS and GARCH-MIDAS incorporating time-varying risk aversion as well as range-based CARR, CARR-MIDAS and heterogeneous autoregressive (HAR), for forecast horizons of 1 day up to 3 months. This result is robust to alternative risk aversion measure, alternative MIDAS lags as well as alternative out-of-sample periods. Overall, our findings highlight the value of incorporating intraday information and time-varying risk aversion for forecasting the renminbi exchange rate volatility.     

Forecasting the Chinese stock market volatility with international market volatilities: The role of regime switching

The purpose of this paper is to investigate the role of regime switching in the prediction of the Chinese stock market volatility with international market volatilities. Our work is based on the heterogeneous autoregressive (HAR) model and we further extend this simple benchmark model by incorporating an individual volatility measure from 27 international stock markets. The in-sample estimation results show that the transition probabilities are significant and the high volatility regime exhibits substantially higher volatility level than the low volatility regime. The out-of-sample forecasting results based on the Diebold-Mariano (DM) test suggest that the regime switching models consistently outperform their original counterparts with respect to not only the HAR and its extended models but also the five used combination approaches. In addition to point accuracy, the regime switching models also exhibit substantially higher directional accuracy. Furthermore, compared to time-varying parameter, Markov regime switching is found to be a more efficient way to process the volatility information in the changing world. Our results are also robust to alternative evaluation methods, various loss functions, alternative volatility estimators, various sample periods, and various settings of Markov regime switching. Finally, we provide an extension of forecasting aggregate market volatility on monthly frequency and observe mixed results.     

Forecasting stock market volatility: Can the risk aversion measure exert an important role?

In this paper, we predict realized volatility of stock return by utilizing time-varying risk aversion based on a simple linear autoregressive model. Our in-sample results suggest that time-varying risk aversion have significant impact for stock return volatility. In terms of out-of-sample forecasting performance, the empirical results indicate that the incorporation of time-varying risk aversion in the benchmark model can yield more accurate stock return volatility forecasts. Notably, the out-of-sample forecasting results confirm that our conclusions are robust when we apply alternative lag orders and alternative prediction evaluation periods. Finally, we study links between the prediction ability of time-varying risk aversion and the volatility of other stock indices and two kinds of crude oil, and find that the new predictor can effectively strengthen forecasting performance in most case. In view of the importance of volatility risk in the asset pricing process, our research is of great significance for financial asset participants.     

Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities

This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.     

The uncertainty in extreme risk forecasts from covariate-augmented volatility models

For a GARCH-type volatility model with covariates, we derive asymptotically valid forecast intervals for risk measures, such as the Value-at-Risk or Expected Shortfall. To forecast these, we use estimators from extreme value theory. In the volatility model, we allow for leverage effects and the inclusion of exogenous variables, e.g., volatility indices or high-frequency volatility measures. In simulations, we find coverage of the forecast intervals to be adequate for sufficiently extreme risk levels and sufficiently large samples, which is consistent with theory. Finally, we investigate if covariate information from volatility indices or high-frequency data improves risk forecasts for major US stock indices. While—in our framework—volatility indices appear to be helpful in this regard, intra-day data are not.     

Forecasting volatility with time-varying leverage and volatility of volatility effects

Predicting volatility is of primary importance for business applications in risk management, asset allocation, and the pricing of derivative instruments. This paper proposes a measurement model that considers the possibly time-varying interaction of realized volatility and asset returns according to a bivariate model to capture its major characteristics: (i) the long-term memory of the volatility process, (ii) the heavy-tailedness of the distribution of returns, and (iii) the negative dependence of volatility and daily market returns. We assess the relevance of the effects of “the volatility of volatility” and time-varying “leverage” to the out-of-sample forecasting performance of the model, and evaluate the density of forecasts of market volatility. Empirical results show that our specification can outperform the benchmark HAR–GARCH model in terms of both point and density forecasts.     

Forecast on silver futures linked with structural breaks and day-of-the-week effect

Silver future is crucial to global financial markets. However, the existing literature rarely considers the impacts of structural breaks and day-of-the-week effect simultaneously on the volatility of silver future price. Based on heterogeneous autoregressive (HAR) theory, we establish six new type heterogeneous autoregressive (HAR) models by incorporating structural breaks and day-of-the-week effect to forecast the volatility. The empirical results indicate that new models’ accuracy is better than the original HAR model. We find that structural breaks and the day-of-the-week effect contain much forecasting information on silver forecasting. In addition, structural breaks have a positive effect on the silver futures’ volatility. Day-of-the-week effect has a significantly negative influence on silver futures’ price volatility, especially in the mid-term and the long-term. Our works is the first to combine the structural breaks and day-of-the-week effect to identify more market information. This paper provides a better forecasting method to predict silver future volatility.     

The role of oil futures intraday information on predicting US stock market volatility

This study investigates the role of oil futures price information on forecasting the US stock market volatility using the HAR framework. In-sample results indicate that oil futures intraday information is helpful to increase the predictability. Moreover, compared to the benchmark model, the proposed models improve their predictive ability with the help of oil futures realized volatility. In particular, the multivariate HAR model outperforms the univariate model. Accordingly, considering the contemporaneous connection is useful to predict the US stock market volatility. Furthermore, these findings are consistent across a variety of robust checks.     

Evolving United States stock market volatility: The role of conventional and unconventional monetary policies

Despite the econometric advances of the last 30 years, the effects of monetary policy stance during the boom and busts of the stock market are not clearly defined. In this paper, we use a structural heterogeneous vector autoregressive (SHVAR) model with identified structural breaks to analyse the impact of both conventional and unconventional monetary policies on U.S. stock market volatility. We find that contractionary monetary policy enhances stock market volatility, but the importance of monetary policy shocks in explaining volatility evolves across different regimes and is relative to supply shocks (and shocks to volatility itself). In comparison to business cycle fluctuations, monetary policy shocks explain a greater fraction of the variance of stock market volatility at shorter horizons, as in medium to longer horizons. Our basic findings of a positive impact of monetary policy on equity market volatility (being relatively stronger during calmer stock market periods) are also corroborated by analyses conducted at the daily frequency based on an augmented heterogeneous autoregressive model of realised volatility (HAR-RV) and a multivariate k-th order nonparametric causality-in-quantiles framework. Our results have important implications both for investors and policymakers.     

Empirical analysis of long memory,leverage, and distribution effects for stock market risk estimates

In this study, eight generalized autoregressive conditional heteroskedasticity (GARCH) types of variance specifications and two return distribution settings, the normal and skewed generalized Student's t (SGT) of Theodossiou (1998), totaling nine GARCH-based models, are utilized to forecast the volatility of six stock indices, and then both the out-of-sample-period value-at-risk (VaR) and the expected shortfall (ES) are estimated following the rolling window approach. Moreover, the in-sample VaR is estimated for both the global financial crisis (GFC) period and the non-GFC period. Subsequently, through several accuracy measures, nine models are evaluated in order to explore the influence of long memory, leverage, and distribution effects on the performance of VaR and ES forecasts. As shown by the empirical results of the nine models, the long memory, leverage, and distribution effects subsist in the stock markets. Moreover, regarding the out-of-sample VaR forecasts, long memory is the most important effect, followed by the leverage effect for the low level, whereas the distribution effect is crucial for the high level. As for the three VaR approaches, weighted historical simulation achieves the best VaR forecasting performance, followed by filtered historical simulation, whereas the parametric approach has the worst VaR forecasting performance for all the levels. Furthermore, VaR models underestimate the true risk, whereas ES models overestimate the true risk, indicating that the ES risk measure is more conservative than the VaR risk measure. Additionally, based on back-testing, the VaR provides a better risk forecast than the ES since the ES highly overestimates the true risk. Notably, long memory is important for the ES estimate, whereas both the long memory and the leverage effect are crucial for the VaR estimate. Finally, via in-sample VaR forecasts in regard to the low level, it is found that long memory is important for the non-GFC period, whereas the distribution effect is crucial for the GFC period. On the other hand, with regard to the high level, the distribution effect is crucial for both the non-GFC and the GFC period. These results seem to be consistent with those found in the out-of-sample VaR forecasts. In accordance with these results, several important policy implications are proposed in this study.     

The term structure of volatility predictability

Volatility forecasting is crucial for portfolio management, risk management, and pricing of derivative securities. Still, little is known about the accuracy of volatility forecasts and the horizon of volatility predictability. This paper aims to fill these gaps in the literature. We begin this paper by introducing the notions of spot and forward predicted volatilities and propose describing the term structure of volatility predictability by spot and forward forecast accuracy curves. Then, we perform a comprehensive study of the term structure of volatility predictability in stock and foreign exchange markets. Our results quantify the volatility forecast accuracy across horizons in two major markets and suggest that the horizon of volatility predictability is significantly longer than that reported in earlier studies. Nevertheless, the aforesaid horizon is observed to be much shorter than the longest maturity of traded derivative contracts.